Hooking into user_admin_menu fails to add menu.

I’m trying to create a custom menu visible to multisite users without a blog. I already have a working minimal test, which I can display to users with a blog:

add_action('admin_menu', 'test_user_admin_menu');
function test_user_admin_menu() {
    add_menu_page('Test Menu', 'Test Menu',
        null, 'test', 'test_user_admin_page');
}
function test_user_admin_page() {
    echo "<h2>Hello world</h2>";
}

Based on codex, to make this menu appear to network users without a blog I need to hook into user_admin_menu action. I verified that I’m using the right hook by changing the first line of the above code to:

add_action('user_admin_menu', 'test_user_admin_page');

This does produce “Hello world” heading on loading dashboard for such user. However, changing the line to:

add_action('user_admin_menu', 'test_user_admin_menu');

produces no menu or output of any kind….

Where am I going wrong? Could somebody please give me a clue?